Plot the Planck Thermodynamic Potential of Water 

Obtain entropy, internal energy, and specific volume of water at various temperatures and pressures.

In[1]:=

X temperature = UnitConvert[ Quantity[Table[x, {x, 20., 400, 20}], "DegreesCelsius"], "Kelvins"]; pressure = Quantity[Table[10^x, {x, 3, 6, 0.2}], "Pascals"]; opt = {"Temperature" -> temperature, "Pressure" -> pressure}; s = ThermodynamicData["Water", "Entropy", opt]; u = ThermodynamicData["Water", "InternalEnergy", opt]; v = ThermodynamicData["Water", "SpecificVolume", opt];

Use the relation to generate discrete values and perform 3D interpolation for the Planck potential or Gibbs free entropy.

In[2]:=

X ifun = Interpolation[Flatten[Table[{{temperature[[j]], pressure[[i]]}, s[[i, j]] - pressure[[i]]*(v[[i, j]]/temperature[[j]]) - u[[i, j]]/temperature[[j]]}, {i, Length[pressure]}, {j, Length[temperature]}], 1]];

Plot the interpolated function as a function of temperature and pressure.

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In[3]:=

X fun[t_?NumericQ, p_?NumericQ] := QuantityMagnitude[ Quiet[ifun[Quantity[t, "DegreesCelsius"], Quantity[p, "Pascals"]] ] ]; Plot3D[fun[tt, p*10^3]/1000, {tt, 20, 400}, {p, 1, 10^3}, AxesLabel -> {Style["Deg. Celsius", 14], Style["KPa.", 14], Style["KJ/(kg.K)", 14]}, Mesh -> None, ImageSize -> Medium, Filling -> Axis]

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